AbstractThis work is mainly
based on quantum game-theoretic techniques and their application to
quantum information theory.Quantum game theory is an important
development in quantum computation and may have implications for
quantum information and quantum communication.The e􀀞ect of quantum
memory on quantum games have been studied.Three di􀀞erent games such
as, Prisoner’s Dilemma, Battle of the Sexes and Chicken have been
analyzed in the quantum domain. By considering the restricted game
situation, it is shown that the e􀀞ects of quantum memory and
decoherence become e􀀞ective in a maximally entangled case.For which
the quantum player can out perform the classical player in all the
three games. It is also shown that the quantum player enjoys an
advantage over the classical player in Battle of the Sexes game for
the amplitude-damping and the depolarizing channels.The quantum
memory compensates the reduction in player’s payo􀀞s due to
decoherence. It has no e􀀞ect on the Nash equilibria of the three
games.
A generalization of two-player quantization scheme to a three-player
Prisoner’s Dilemma game under the e􀀞ect of correlated noise is also
presented.In a restricted game scenario, it is shown the quantum
player is always better for all values of the decoherence
parameter for the entire range of memory parameter.It is seen
that for maximum degree of correlation, the game does not become
noiseless and quantum player can still outscore the classical
players for the entire range of the decoherence parameter 􀁳􀀾
producing an interesting result in comparison with a two-player
quantum game.It is also shown that correlated noise has no e􀀞ect on
the Nash equilibrium of the game.
By exploiting the three-player quantization scheme, we have studied
the communication aspects of a three-player Prisoner’s Dilemma
quantum game. It is shown that entanglement plays a dominant role in
a three-player quantum game.On the basis of initial state and the
measurement basis entanglement parameters, a relation among
different payo􀀞s is established.It is investigated that the
strategies of the players act as information carriers in quantum
games. A relationship for the information shared among the parties
is also established.
A scheme for quantum key distribution is proposed in which a secret
key can be generated from the data coming through a partially
entanglement breaking channel.This scheme is rather deterministic
and e􀀡cient in the sense that two classical bits can be transferred
per entangled pair of qubits.Furthermore, it is important to point
out that, in this scheme, same symbol can be used for Eve’s
detection and key generation. It is also worth noting that the
eavesdropper, Eve, can be detected very easily from the disturbance
of the elements of the decoding bimatrix. We have checked for the
security of the scheme and found it secure against individual
attacks.
It is further investigated that quantum games are useful in
developing quantum cryptographic protocols.A multiparty quantum
cryptographic protocol using tripartite entangled GHZ states is
devised using game-theoretic techniques.In this protocol, two
classical bits can be transferred per entangled pair of qubits to
the communicating parties.Unitary operators applied by the sender on
a tripartite entangled state encodes a classical symbol that can be
decoded at receiver’s end with the help of a decoding matrix. In
this protocol, if Eve interferes during the transmission, she can be
detected by the disturbance of the decoding matrix. Our security
analysis shows that this protocol is also secure against
intercept/re-send attacks.